The Group H encounter was a perfect opportunity for Stramaccioni to reintegrate the Holland midfielder into his plans amid speculation he is being excluded for refusing to take a pay cut.
Stramaccioni has not picked the 28-year-old since September and reacted with fake surprise to reporters who queried Sneijder's conspicuous absence from Thursday's squad list.
"I wasn't expecting any questions about Sneijder! Really, you've taken me totally by surprise," he joked.
"I think I've already talked extensively about this topic and the president (Massimo Moratti) has spoken on several occasions.
"All the decisions now and in the future, concerning all Inter players, are based on my own assessments. Therefore, Sneijder's involvement is up to me.
"He's well, happy, and training with his team-mates. So I'll ask you not to question me about it again.
"I repeat, I make my choices and I take all responsibility."
The Nerazzurri are already through to the last 32 as group runners-up behind Rubin Kazan, but they have struggled at the San Siro, winning just one European game in Milan this season.
Marko Livaja has been a regular starter in the Europa League and the 19-year-old striker admitted his surprise at playing so many minutes.
"I didn't expect any of this," he told inter.it. "I always just wanted to work hard so I could give 100 per cent any time I was called into action."
Neftchi have won only two of 20 away fixtures in European competition in their history, losing 15, but the Azerbaijanis have the chance to finish third if they better Partizan Belgrade's result at home to Rubin.